Fire Beam or Fire Bomb. Throw fires everywhere before the ship explodes. Try to hit the crew last because once they die, the fight ends and you can no longer target the ship.

Astronomically Low Odds

Fail to evade 5 shots in a row with a fully powered and upgraded engine.

BOARDING OBJECTIVE SUCCESSFUL

Have a single boarding drone kill 4 crewmembers on one ship.

They never saw it comming

Use the Weapon Pre-Igniter augmentation to destroy an enemy ship in one volley before the enemy can get a single shot off.

Glaive Beam and/or Hull Missiles may help.

Trustworthy Auto-Pilot

Defeat an enemy ship with all of your crew aboard it.

See the second Mantis ship. You could also get this with any ship simply by throwing all your crew into it before you kill the enemy crew. Upgraded teleport or Heal Bombs might help.

Slice and Dice

Hit every room of a ship with at least one beam in under 5 seconds.

Best targets are the small Slug ships or small automated crafts. Artillery beam helps,but using multiple beams on an unshielded Auto-Scout is by far the easiest.

Victory through Asphyxiation

Empty the oxygen (Net level less than 5 percent) of a non-automated, hostile enemy ship.

Slug Interceptors are the best target for this. The Oxygen system for that ship is separated from the rest of the ship, so the crew can't even reach it repair it. Just nuke it then wait for them to suffocate. 1 missile or bomb and you're done.

You need one crew member from each race. The Human counts as 1, meaning 5 aliens, actually. This is somewhat easier to complete in the Kestrel B, because your starting crew includes three of the six required races.

Full Arsenal

Have every system and subsystem installed on the Kestrel Cruiser at one time.

Only the Teleporter, Cloak and Drone systems are missing when you start the game.

Tough Little Ship

As the Kestrel Cruiser, repair back to full health when it only has 1 HP remaining.

Find an asteroid field near a store. Make sure you have enough scrap to repair all damage and ensure the path to the store is clear. At the asteroid field, drop your shield and let the asteroids hit you. When you reach 2 HP, wait for the next asteroid. When you see it, activate your shields before it hits. They take some time to actually activate and protect from further damage.

A safer, more sure way is with a controlled burn using Fire Bomb. Stop 1 jump short of a store, getting some damage along the way. It does NOT count if you reduce your hull to 1 while you are AT the store. Lower your shields. Use firebomb to hit your own shield room and open the door so it can spread to medical. Each system destroyed reduces your hull by 1. When the fire has destroyed those two systems, put the fires out by venting. Then let the oxygen recharge and repair the systems. Repeat as needed. Note: it goes faster if you upgrade your oxygen to level 2 and you should have doors at least level 2 to keep the fire from getting out of hand..

Destroy a ship at full health during a single cloak in the Stealth Cruiser.

Upgrade your cloak to the highest level as soon as you can. With this cloak, your pre-installed weapons can fire two volleys at this level. This is more than enough to take out the unshielded Auto-Scouts.

Phase Shift

With the Stealth Cruiser, avoid 9 points of damage during a single cloak.

In essence, this means finding an enemy ship that can potentially deal 9+ damage in a single volley. This can easily be done against the Rebel Flagship's third stage.

Tactical Approach

With the Stealth Cruiser, get to sector 8 without jumping to a beacon with an environmental danger.

Jumping to a regular nebula beacon will not prevent you from getting this achievement.

Kill 5 enemy crew in a fight without taking hull damage or losing a crew member while using the Mantis Cruiser.

Find a high level ship that has many crew members, and use advanced shields, along with defense drones. You could also disable their weapons early into a fight.

Battle Royale

While using the Mantis Cruiser, kill the last enemy with your last crew member on their ship.

If you find a ship with 2 crewmembers, this is quite easy. Send over two of your crew, and have one of them fight the two enemies. As you do this, open the airlocks and subject them to zero oxygen, killing them. With your first away team member dead, send in the second. Mantises should be easily able to do this.

With the Engi Cruiser, destroy an enemy ship using only drones (no weapons).

The Torus starts with an Anti-Ship I drone. Activate it against an unshielded Auto-Scout, occasionally found at the start of the game. Alternately, you could just use the drone in an asteroid field. The rocks and drone will be too much for a single shield bubble to stop. But this tactic runs the risk of wasting drones because rocks sometimes crash into them and wreck the drone.

The guns... They've stopped

Have 4 enemy systems or subsystems ioned at the same time while using the Engi Cruiser.

Buying an additional Ion Blast II, or two additional Ion Blast I will help with this. Also, enemy systems with cooldown (e.g. cloak or teleporter) ionize themselves after use, and will count as one of the four systems. Alternatively you could jump to a pulsar in advanced edition and wait.